AP Physics ST Induced emf and Electric Fields

Induced Electric Fields Increase the magnetic field at a steady rate the flux through a conducting ring will change. 1.By Faraday’s Law an emf is induced in the conducting ring. 2.By Lenz’s Law the induced current is counterclockwise.

Induced Electric Fields The changing flux inducing a current implies the presence of an electric field. This electric field has two VERY important properties: 1.E is non-conservative. 2.E varies with time. conducting ring

Induced Electric Fields INTERESTING FEATURE – There is an electric field induced in the region of changing flux even if there is no conductor!! – MEANING … a free charge placed in a changing B will experience an E! NO conducting ring

Induced Electric Fields If the magnetic field varies with time an electric field is induced. Recall: The induced E is tangent to a circle of radius r at all points according to Lenz’s Law.

Induced Electric Fields If the rate of change of B is INCREASING into the page… – E is counter-clockwise If the rate of change of B is DECREASEING into the page… – E is clockwise

Faraday’s Law Restated Evidence suggests that the induced emf is related to the electric field. This understanding is realized in the … General Form of Faraday’s Law

Faraday’s Law Restated Consider a test charge traveling around the circular path. Work is done on this charge by the electric force. – Does the magnetic force do work on the test charge?

Faraday’s Law Restated Work on the test charge is equivalent to … Recall… General definition of work…

Faraday’s Law Restated Work done by the electric field around the circle once… “equivalating”… (yes it’s a word… I made it) Resulting in…

Faraday’s Law Restated The cool thing is that this path does NOT need to be circular! – The emf for ANY closed loop path requires only the line-integral over that path. – Also note that work is only done when the component of E is along the direction of displacement; hence the dot product.

Faraday’s Law Restated No longer does one need the current to speak about the induced emf. The magnitude of the induced emf is proportional to the sum of all contributions of E along the closed path. – Also equivalent to the negative rate of change of external magnetic flux.

Faraday’s Law Restated This is referred to as the General Form of Faraday’s Law… IMPORTANT NOTES: 1.The induced electric field can’t possibly be a conservative field (like an electrostatic field) because the line integral over a closed loop would equal ZERO!!

Faraday’s Law Restated 2.THIS induced electric field is a result of the time rate of change of the magnetic flux… E varies with time!

Lesson Summary

Example #1 Consider a region of varying magnetic field and four similar closed loop paths that enclose identical areas. Rank the paths of induced emf; greatest first

Example #2: Serway 5 th ed For the situation described in the figure below, the magnetic field changes with time according to the expression… and r 2 = 2R = 5.00 cm. a.Calculate the magnitude and direction of the force exerted on an electron located at point P 2 when t = 2.00 s. b.At what time is this force equal to zero? P2P2 R

Example #3: Serway 5 th ed A solenoid has a radius of 2.00 cm and 1,0000 turns per meter. Over a certain time interval the current varies with time according to the expression, where I is in amperes and t is in seconds. Calculate the electric field 5.00 cm from the axis of the solenoid at t = 10.0 s.